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The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
Solving equations
From the question, we are to determine how much money there are in each box
From the given information,
"Debbie has 340 dimes in three boxes"
Let x represents the number of dimes in the first box
y represent the number of dimes in the second box
and z represent the number of dimes in the third box
Thus,
x + y + z = 340
Also, from the given information
"she says that there are 4 times as many dimes in the first box as in the second"
x = 4y
and
"3 times as many in the third box as in the first"
z = 3x
Substitute the second and third equations into the first equation
x + y + z = 340
4y + y + 3x = 340
4y + y + 3(4y) = 340
4y + y + 12y = 340
17y = 340
y = 340/17
y = 20
Substitute the value of y into the second equation
x = 4y
x = 4(20)
x = 80
Substitute the value of x into the third equation
z = 3x
z = 3(80)
z = 240
Thus,
There are 80 dimes in the first box
80 dimes = 8 dollars
There are 20 dimes in the second box
20 dimes = 2 dollars
There are 240 dimes in the third box
240 dimes = 24 dollars
Hence,
The amount of money in the first box is 8 dollars
The amount of money in the second box is 2 dollars
The amount of money in the third box is 24 dollars
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